In the given figure, AB is parallel to CD. Angle PAB = 65 degrees and angle DCP = 110 degrees. What is the value (in degrees) of angle APC?

Correct option is C

Given:

AB ∥ CD

∠PAB = 65°

∠DCP = 110°

Find ∠APC

Concept Used:

Angles on a straight line sum to 180°.

Parallel line angle properties.

Formula Used:
Angle at vertex = 180° − (sum of inclinations with parallel lines)

Solution:

Since AB ∥ CD:

Line AP makes an angle of 65° with the horizontal line AB.

At point C:

Given ∠DCP = 110°

So, the acute angle between CP and CD is:

180° − 110° = 70°

Now at point P:

The two slant lines make angles 65° and 70° with the parallel horizontal lines.

Therefore,

∠APC = 180° − (65° + 70°)

= 180° − 135°

= 45°

Therefore,

∠APC = 45°